STAT 5.7-8

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population's distribution, as long as the sample size is sufficiently large (usually n ≥ 30).

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a statistic (like the sample mean) obtained from a large number of samples drawn from a specific population.

Front

What does it mean for a distribution to be skewed?

Back

A distribution is skewed if it is not symmetrical, meaning that one tail is longer or fatter than the other. Right skewed means the tail on the right side is longer, while left skewed means the tail on the left side is longer.

Front

What is the mean of a sampling distribution?

Back

The mean of a sampling distribution is equal to the mean of the population from which the samples are drawn.

Front

What is the standard deviation of a sampling distribution called?

Back

The standard deviation of a sampling distribution is called the standard error.

Front

How do you calculate the standard error?

Back

The standard error (SE) is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n): SE = σ / √n.

Front

What is the significance of a sample size of 30 in statistics?

Back

A sample size of 30 is often considered the threshold for the Central Limit Theorem to apply, meaning the sampling distribution of the sample mean will be approximately normal.

Front

What is the formula for the mean of the difference between two sample means?

Back

The mean of the difference between two sample means (X̄1 - X̄2) is equal to the difference between their population means (μ1 - μ2).

Front

What is the relationship between sample size and standard error?

Back

As the sample size increases, the standard error decreases, indicating that larger samples provide more accurate estimates of the population mean.

Front

What does it mean to be '1.77 standard deviations above the mean'?

Back

Being '1.77 standard deviations above the mean' indicates that a value is 1.77 times the standard deviation greater than the average value in a distribution.